Venn diagrams: set notation

The Maths Habit

One of these means and. One means or. Which picture goes with which?

∩ ∪

ξAB
1A ∩ B
ξAB
2A ∪ B

Which numbers are in both lists?

{2, 4, 6, 8} and {4, 5, 6}4, 6{1, 3, 5, 7} and {3, 6, 9}3{1, 2, 3, 4} and {2, 4, 6, 8}2, 4

Set
A group of numbers or things. We list them inside curly brackets { }.
ξAB
ξ
Everything in the question. It is the whole box.
ξAB
A ∩ B
In A and B. Say “A intersection B”.
ξAB
A ∪ B
In A or B or both. Say “A union B”.
ξAB
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 2, 5, 7}B = {2, 3, 7}
ξAB15273468
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {3, 4, 6}B = {1, 4, 8}
ξAB36418257
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 2, 5, 7}B = {2, 3, 7}
ξAB15273468
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
1Put the numbers in both in the middle.2Put the rest in the circles.3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 5, 6, 9}B = {5, 7, 9}
ξAB265971348
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 2, 5, 7}B = {2, 3, 7}
ξAB15273468
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
1Put the numbers in both in the middle.2Put the rest in the circles.3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 6, 8}B = {3, 4, 8}
ξAB168342579
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 2, 5, 7}B = {2, 3, 7}
ξAB15273468
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.
1Put the numbers in both in the middle.2Put the rest in the circles.3Put the numbers left outside.
Fill in the Venn diagram.ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {3, 4, 7, 10}B = {4, 6, 10}
ξAB37410612589
1Put the numbers in both in the middle.
2Put the rest in the circles.
3Put the numbers left outside.

4List the numbers you want.
A ∩ Bin A and B
ξAB
A ∪ Bin A or B or both
ξAB

The middle, or all of both circles?

A ∩ Bthe middleA ∪ Bboth circlesin A or B or bothboth circlesin A and Bthe middle
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 3, 4, 6}B = {3, 6, 8}
ξAB14368257
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={3, 6}
A ∪ Bin A or B or both={1, 3, 4, 6, 8}
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {2, 5, 7}B = {1, 5, 6}
ξAB27516348
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={5}
A ∪ Bin A or B or both={1, 2, 5, 6, 7}
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 3, 4, 6}B = {3, 6, 8}
ξAB14368257
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={3, 6}
A ∪ Bin A or B or both={1, 3, 4, 6, 8}
1Put the numbers in both in the middle.2Put the rest in the circles.3Put the numbers left outside.4List the numbers you want.
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {4, 5, 8}B = {2, 5, 8, 9}
ξAB458291367
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={5, 8}
A ∪ Bin A or B or both={2, 4, 5, 8, 9}
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 3, 4, 6}B = {3, 6, 8}
ξAB14368257
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={3, 6}
A ∪ Bin A or B or both={1, 3, 4, 6, 8}
1Put the numbers in both in the middle.2Put the rest in the circles.3Put the numbers left outside.4List the numbers you want.
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 3, 6, 7}B = {6, 9}
ξAB137692458
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={6}
A ∪ Bin A or B or both={1, 3, 6, 7, 9}
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 3, 4, 6}B = {3, 6, 8}
ξAB14368257
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={3, 6}
A ∪ Bin A or B or both={1, 3, 4, 6, 8}
1Put the numbers in both in the middle.2Put the rest in the circles.3Put the numbers left outside.4List the numbers you want.
List A ∩ B and A ∪ B.ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 9}B = {1, 4, 7, 9, 10}
ξAB24917103568
123Fill in the Venn diagram.
4List the numbers you want.
A ∩ Bin A and B={4, 9}
A ∪ Bin A or B or both={1, 2, 4, 7, 9, 10}

Venn diagrams: set notation worksheet, page 1

Venn diagrams: set notation worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

ξAB16248357

  1. A ∩ B = {2}

    Right

  2. A ∪ B = {2}

    Wrong: that is A ∩ B

  3. A = {1, 6}

    Wrong: A = {1, 2, 6}

  4. A ∪ B = {1, 2, 4, 6, 8}

    Right

  5. B = {2, 4, 8}

    Right

  1. ξ = {1, 2, 3, ..., 10}. A = {2, 4, 6, 8, 10}. A′ means not in A. List A′.

    {1, 3, 5, 7, 9}

  2. ξ = {1, 2, 3, ..., 10}. A = even numbers. B = multiples of 3. One number is picked at random. Find P(A ∪ B).

    710

  3. A Venn diagram shows how many: 5 in A only, 3 in both, 7 in B only, 5 outside. Find P(A ∩ B).

    320

  1. Fill in the Venn diagram. List A ∩ B.

    {4, 6}
    ξAB46ξ = {1, 2, ..., 8}A = {1, 4, 6}B = {3, 4, 6, 7}A ∩ B ={}in A and B

  2. Fill in the Venn diagram. List A ∪ B.

    {2, 3, 5, 8, 9}
    ξABξ = {1, 2, ..., 9}A = {2, 3, 8}B = {3, 5, 9}A ∪ B ={}in A or B or both

  3. ξ = {1, 2, ..., 10}, A = {1, 5, 6, 10}, B = {2, 5, 10}. List A ∪ B.

    {1, 2, 5, 6, 10}
    ξAB
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